Spot filmer cassette transport vibration support

ABSTRACT

A system and method is disclosed for minimizing residual vibration of a radiographic system due to rapid movement of a radiographic film cassette between a park and expose position. The cassette is moved by a servo system including a servo motor which is responsive to a voltage input waveform to drive the cassette. A waveform is chosen for the voltage input such that no impulse derivatives appear until the waveform has been differentiated at least three times. The primary natural resonant frequency of the system is determined and noted. The duration of the selected input waveform is adjusted such that the frequency spectrum of the adjusted input waveform defines a relative null which approximately coincides with the primary resonant frequency. The amplitude of the voltage input waveform is then further adjusted as a function of the distance to be traveled by the cassette between the park and expose positions. The servo system can optionally be operated over a portion of the cassette transit in a closed loop fashion. In a mechanical embodiment, sinusoidal cassette acceleration can be effected by the use of a mechanical drive linkage coupled between a motor and the cassette, the drive linkage employing a cycloidal cam and associated cam follower to govern the profile of cassette movement.

This application is a continuation, of application Ser. No. 879,330,filed 6/27/86 which is a continuation, of application Ser. No. 161,416,filed 2-23-88.

TECHNICAL FIELD

This invention relates generally to the field of medical diagnosticimaging x-ray systems, and more particularly to a system and method forreducing residual structural vibration in a spot film device caused byfilm cassette transport motion executed in operation of the device.

BACKGROUND ART

A spot film device is a combination radiographic filmer and fluoroscopicimager. Such devices are commonly mounted for use in conjunction with anx-ray table.

The spot film device includes a housing, sometimes called a "tunnel",which is movably supported on the xray table by a movable column ortower. The tower supports the spot film tunnel component for movementlongitudinally and laterally with respect to the table top in verticallyadjustable planes that are parallel to the table top. An x-ray source islocated within the table body and is mechanically coupled to move inunison with the longitudinal and lateral motion of the spot film device.The source propagates x-rays from within the table body, upwardlythrough the table top and through the body of a patient when positionedon the table top. The pattern of radiation emergent from the uppersurface of the patient's body defines an image of the patient's anatomy.

The rear portion of the tunnel nearest the tower, defines a parkingspace or position for a radiographic film holding cassette which is usedin connection with the radiographic filming function of the spot filmdevice. Transport means is provided for mounting a film cassette formotion between the parking position and an active filming, or "expose",position, more distant from the fluoro screen or image amplifier. Thetransport mechanism includes manual, or electromechanical servo, powermeans, the latter of which, on command, projects the film cassettebearing a portion of radiographic film into the x-ray path exposeposition to take radiographs of selected images that are detected in thefluoroscopic mode. After each radiograph is taken, the cassette isreturned to the park position, and the spot film device continues fluoromode operation.

The general technology relating to spot filming devices is well known.The following U.S. patents, here expressly incorporated by reference,disclose details of typical spot film devices: Stava et al., U.S. Pat.Nos. 2,767,323; Stava et al., 2,749,445; Barrett et al., 3,173,008; andHunt, 4,357,538.

The spot film device thus facilitates selected clinical observationsmade during fluoroscopy to be permanently recorded on film. The speed ofcassette transport between these two positions is of great clinicalimportance, due to involuntary physiological movement within thepatient's body, such as peristalsis. It is important that this transporttime be as short as possible to permit accurate representation on filmwithout blurring or altogether missing an observation. While strivingfor minimal transport time, it is nonetheless necessary to alsominimize, or avoid altogether, vibration of the structure supporting thespot film device, which vibration is caused by the quick transport ofthe film cassette between the park and expose positions. This structuralvibration, if uncontrolled, can cause blurred images on the film,diminishing their diagnostic usefulness.

Prior methods of cassette transport control include various forms ofspeed control which attempt to shorten transport time. Other proposalshave included force buffering, which attempts to control structuralvibration. All prior methods of cassette transport, however, fall shortof providing an effective comprehensive solution because none addressthe complete problem of system dynamics, i.e., the synergisticinteraction of the spot filmer and its associated support structure.

One technique for operating a cassette transport servomechanism is toabruptly apply to a servo drive motor of a spot film device a squarewave voltage input and to abruptly terminate the square wave inputapplication, such as by way of a limit switch, when the cassetteapproaches or reaches the end of its predetermined travel path. Thistechnique, however, due to the abruptness of the application and removalof the voltage input, produces significant residual vibration in thestructural components of the spot filmer system, such as in the supporttower, which is unacceptable for reasons noted above. Therefore, theproposed square wave input method, sometimes called "bang-bang", failsto deal effectively with accommodation of control of the mechanicalstructural dynamics, either as an integral part of the control strategyor otherwise, to minimize structural motion and improve film imageresolution and quality.

It has been proposed, in general industrial servo mechanism technology,to apply mechanical means, such as cams, to mechanical linkages fordriving movable components, to reduce vibration attendant upon movingthe component from one position to another along a predetermined travelpath. Such techniques, however, address only the particular aspect ofmechanical control, and do not address the aspect of input commandsignals to the servomechanism drive motor. Thus, such a purelymechanical approach is not entirely satisfactory in reducing vibration,inasmuch as it does not consider and accommodate the particularattributes of the total system.

In mechanical general industrial embodiments, mechanical means have beenprovided to impart a generally trapezoidal acceleration profile tomotion of a movable component. In such a proposed servo system, thesquare wave voltage input was applied as described above.

In accordance with another proposal, a spot filmer cassette transportservomechanism was provided wherein the voltage input to the servo motordefines a triangular waveform. According to this proposal, the amplitudeof the voltage waveform is modified as a function of the mass of thecassette to be transported, in order to maintain the total transit timefor the cassette motion at a constant value, irrespective of thecassette mass. Vibration suppression is believed to have formed no partof this proposal.

In accordance with still another proposal, a servo mechanism wasprovided for spot filmer cassette transport which includes a number ofinterchangeable cams, each defining a different acceleration profile forcassette movement. The cam is selected depending upon the mass of thecassette to be transported. This proposal, however, does not address theimpact of the input voltage profile on vibration, and thereby does notaddress the total system needs for reduction of residual vibration.

In the absence of effective cassette transport vibration suppression,designers have sometimes compensated by building such systems withhighly rigid support structure, less susceptible to vibration. Thismeasure, however, undesirably increases the weight and cost of systemsof this nature.

A known spot film device, a model 1720A manufactured and sold by PickerInternational, of Cleveland, Ohio, U.S.A., employs a servo motor toprovide film cassette motion. The motor control provides an inputvoltage to the motor which is a ramp function, in an attempt to reduceresidual vibration. As is the case of the other attempts describedabove, this particular prior art attempt, while helpful to a degree,represents an incomplete solution to the vibration problem. The inputvoltage profile is not specifically tailored to the mechanical system.

Another prior art spot film device, designated model 1717, manufacturedand sold by Picker International, Cleveland, Ohio, U.S.A., utilizes arotating arm mechanism to provide film cassette motion. Mechanisms suchas these, however, are mechanically complex and make optimizing motionforces difficult.

A general object of this invention is to provide a spot film device inwhich the electrical servo input, servo cassette transport systemradiographic system structure, and the cassette itself are all mutually"tuned" to one another to reduce or eliminate residual vibration fromcassette transport motion.

DISCLOSURE OF THE INVENTION

The disadvantages of the prior art are reduced or eliminated inaccordance with the present invention by the use of a method and systemfor controlling motion of a movable component of an imaging systememploying penetrative radiation. The system includes support structure,and means for defining a travel path for the component between first andsecond positions along the path. The system further includes servo meansresponsive to an electrical input signal for driving the component alongthe path between the two positions.

A method in accordance with the present invention begins with the stepof determining the primary resonant natural frequency of the vibratoryresponse characteristic of the total system, taking into account themass of the movable component, as well as the remainder of the system.This done, the next step is to define, in the time domain, a firstfunction describing a preferred pattern of motion of the componentbetween the first and second positions. This first function ischaracterized by the absence of an impulsive derivative in any order ofderivative less than the second derivative of acceleration of thedefined component motion.

Next, one defines the transit time T for the component between the firstand second positions, as a second function, this one being a function ofthe primary resonant natural frequency, such that this second functiondefines, in the frequency domain, a first relative null substantiallycoincident with the primary natural resonant frequency. This step ofdefining the transit time T is performed upon the time domain functionderived in the previous step.

Next, the amplitude of the velocity profile, in the time domain, definedby the first function is further adjusted as a function of the distancebetween the first and second positions along the component travel path.The above definitions being accomplished, an input voltage waveform isapplied to the servo system which has substantially the same time domainconfiguration as the adjusted velocity profile obtained in the previoussteps.

This method, and the employment of means for implementing it,substantially reduces, or eliminates altogether, residual vibration inthe system which would otherwise result from component motion. Thesystem can be made of elements which are less massive and heavy than arenecessary in the prior art, since it is no longer necessary for thesupport structure to suppress vibration, the vibration being eliminatedbefore it begins by the unique design of the voltage input profile inaccordance with this invention.

In accordance with a more specific embodiment, this invnetion ispracticed in the context of a radiographic imaging system including aspot filmer having means for transporting a radiographic film cassettebetween park and expose positions.

In accordance with another specific embodiment, the first function inturn defines an acceleration profile of the movable component which issubstantially trapezoidal in shape. This implies that the voltage inputto the servo system is substantially triangular in shape.

In accordance with another specific embodiment, the second function, asdefined above, between transit time T and the primary natural resonantfrequency f, is in the form of:

    T=a+bf+cf.sup.2 +df.sup.3 + . . . +nf.sup.m.

Other features and aspects of the present invention will become apparentfrom a study of the following detailed description, and from thedrawings, in which:

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a perspective view illustrating a radiographic imaging systemincorporating the present invention;

FIG. 2 is a combination plan/block diagram illustrating a portion of thesystem of FIG. 1;

FIGS. 3-5 are block diagrams illustrating a manner of implementing anembodiment of the present invention;

FIG. 6 is a collection of plots of frequency domain graphs illustratinga manner of implementation of the present invention;

FIGS. 7 and 8 and time domain plots illustrating a manner ofimplementation of the present invention;

FIGS. 9 and 10 are further graphical representations of the manner ofimplementing the present invention;

FIGS. 10A and 10B are graphical representations of means employed inimplementing the present invention;

FIG. 11 is a block diagram illustrating an example of a servo controlsystem for use in connection with the present invention;

FIG. 12 is a plan view of a portion of mechanism of another embodimentof the invention.

BEST MODE FOR CARRYING OUT THE INVENTION

FIG. 1 is a perspective view of a typical diagnostic x-ray systemincorporating a spot film device in accordance with the presentinvention. The system includes an x-ray table having a body 10 withinwhich is located an x-ray source, which is not visible. When energized,the x-ray source projects x-rays upwardly through a table top 11 onwhich a patient undergoing x-ray examination may be placed.

The table body 10 is supported on a base 13.

The x-ray source is mounted on a known type of carriage whichfacilitates motion of the source in a direction parallel to thelongitudinal direction of the table top.

Extending upwardly from the carriage at the rear of the table top is atower or column 16 which may be extended and contracted in the verticaldirection, and which is movable in unison with the source.

A spot film device 17 is supported on the column 16 by means of abearing support 18 that cooperates with a pair of tracks, such as onetrack designated by the reference character 19, to enable the spot filmdevice to be moved manually to a limited extent in a directiontransverse to the table top.

Mounted to the top of the spot film device 17 and near its front is afluoroscopic device which is generally designated by the referencecharacter 20. In modern practice it is customary to use an x-ray imageintensifier for fluoroscopy and the use of such a device is assumed inthis case. A television camera, not shown, mounted within a housing 21,is used to display the x-ray image, obtained during a fluoroscopicprocedure, on a television monitor which is not shown in FIG. 1 but iswell known to those of ordinary skill in the art.

A control console for operating the spot film device is located at thefront and is designated by the reference character 22. The spot filmdevice has a front opening 23 for inserting and withdrawing aradiographic film cassette at the front of the table. At the top of thedevice and behind the image intensifier 20 is defined another aperture24 which provides the option of inserting and withdrawing a filmcassette at the rear.

FIG. 2 illustrates in simplified form apparatus for transporting aradiographic film cassette between the park and expose positions, anddrive means for implementing the required movement.

The motion facilitating apparatus comprises, for example, a pair ofparallel rails 50 which extend generally from the park to the exposeposition and are mounted within the housing of the spot film device. Acarriage member 52 is mounted for movably riding upon the rails 50, suchas by flanged wheels or the like (not shown). Upon the carriage 52 canbe positioned a radiographic film cassette 54 of known type. Amechanical drive linkage, shown in block form at 56, is coupled to thecarriage 52 in order to drive the carriage along the rails 50 in adirection indicated by the arrows 58 upon the provision of motive powerto the drive linkage. That motive power is furnished to drive linkage byan electric motor 60, comprising an output shaft 62. The motor and drivelinkage cooperate such that rotation of the output shaft, in directionsindicated by the arrows 64, causes the linear motion of the carriage 52in the directions indicated by the arrows 58.

A reference generator circuit 66 produces an electrical input voltagesignal which is applied to the motor 60. The characteristics of theprofile of the input signal produced by the reference generator 66 willbe described in more detail below.

Thus far, what has been described is an open loop servo system.Optionally, however, and as described in more detail below, a closedloop servo system can be employed. In such a system a position orvelocity detector 70 is coupled to sense position and/or velocity ofmotion of the carriage 52 bearing its cassette 54. The output from theposition detector 70, an electrical signal, is provided to the minusinput of an adder circuit 72, which, in such mode of use, becomes anerror detector, and produces an error signal along a path indicated at74 to govern operation of the motor.

Optionally, a switch 76 can be interposed in the signal path between theposition detector 70 and the adder circuit 72. When the switch 76 ismoved to its left hand position, as shown in FIG. 2, the feedback loopportion of the servo control circuit is broken. When the switch is movedto its right hand position, the closed loop portion of the circuit isoperable in conjunction with the forward path loop. By the use of theswitch 76, manual or automatic control of disablement and enablement ofthe feedback loop portion of the servo circuit can be effective.Utilization of such a technique is described in more detail below.

GENERAL CONSIDERATIONS

An important aspect of this invention is to facilitate fast cassettetransport without blurring of film images due to structural vibration ofthe x-ray examination apparatus. This result is achieved by devising acassette transport system that is governed by unique cassette motionspecification, or mathematical relationship, which tunes the power driveto the x-ray apparatus structure in a specific manner. The controlfunction, i.e., the time domain configuration of the input electricalsignal applied to the servo, is selected to facilitate fast cassettetransport movement with an acceleration profile which is specificallydesigned to avoid excitation of vibratory response of the underlyingsupport structure, i.e., to avoid as far as possible oscillatory swayingof the film relative to the object being examined and, in addition, toavoid movement of the x-ray beam, causing a blurred image.

Given an apparatus consisting of a spot film device supported by someappropriate structure, operation of the cassette transport system withinthe spot film device is governed by a mathematical relationship, i.e., amotion specification, between cassette movement travel time T, and theprimary resonant natural structural vibration frequency f of theapparatus. The cassette movement time is a function of the mass beingtransported, that is, the mass of the cassette and that of the othermovable parts of the carriage structure.

The input control function, which embodies and implements the motionspecification, depends upon the inherent behavior of the frequencydomain spectrum of the vibratory response characteristic of the x-rayexamination apparatus as a whole, where this response is induced byoperation of the cassette transport servo mechanism. The time domainresponse (the vibratory oscillation or residual vibration) of theapparatus to a disturbance input, such as cassette transport, must beanalyzed into its respective frequency components by a FourierTransformation to specify its associated frequency domain spectrum.

Once this frequency domain interpretation of apparatus behavior isachieved a means arises for determining the most appropriate motionspecification, or mathematical expression, for cassette motion. If themotion specification, described by the time domain configuration ofservo input, is poorly chosen, the natural resonant frequency responseof the apparatus will be stimulated by the input and the resultingvibratory output of the apparatus will exhibit undesirable resonantbehavior, yielding detrimental vibration and ultimately a blurred image.

In one embodiment of the present invention, the motion specification isdesigned such that, when analyzed into its frequency components, can beseen to avoid vibratory stimulation at the resonant response natural tothe system, which eliminates residual vibration. Moreover, this inputfunction is further chosen in a manner yielding the fastest possiblecassette transport time T consistent with nullifying apparatus resonantresponse.

In another embodiment of the invention, it is seen that, in principle,the electro-mechanical servo mechanism is operable in an open loopmanner, independently of any feed back signals, thus resulting in a muchsimplified servo mechanism controller. However, this feature does notexclude utilization of classical control theory in the implementation ofthe invention. In this embodiment, the feedback loop signals are placedsubservient to the motion specification here disclosed, during most ofthe cassette transport motion. In such an embodiment, the techniques ofclosed loop servo control could function in a passive monitoring modeduring the major portion of cassette transport, i.e., in open loopfashion, and only in the terminal phases of motion the closed loopfeedback signals are enabled to control the remainder of the cassettetransport motion along its defined path.

This invention possesses the added advantage that the apparatus operatordoes not need to anticipate events and manually command the exposuresequence at an estimated time ahead of the anticipated event, to avoidinvoluntary physiological movement during exposure, or to capture adesignated segment of observation of motion within the patient's body.Because the cassette movement time, in practice of this invention, issufficiently short, (less than approximately three quarters of a second)the time delay between command and exposure is quite short. Moreover,even with this short transport time image blurring as described above isavoided.

At this point, it is desirable to set forth in a general way how onegoes about specifying, or defining, cassette motion in a way whichminimizes residual vibration. As the term implies, "motionspecification" involves independently selecting, or determining, aspecific time domain pattern of cassette motion. The selection of thepattern of motion is not done arbitrarily, but rather with respect toseveral important criteria.

Once the pattern of motion is defined, a voltage waveform is developedin accordance therewith and applied as an input drive voltage into theservo system which drives the cassette.

If one defines any time domain function related to cassette motion, suchas displacement, velocity or acceleration, an entire set ofcorresponding profiles are also uniquely defined, each profilecorresponding to either displacement with respect to time, or one of itshigher order derivatives. For reasons described in more detail below,the inherent qualities of a servo system dictate that the mostappropriate motion related profile to which the voltage input should bematched is the velocity profile with respect to time.

Amont the parameters of the velocity profile which must be selected, orspecified, are (1) the shape of the profile and (2) the width of theprofile, expressed in time, which corresponds to the total time T ofcassette transport between the park and expose positions. One must also,by known means, determine the primary resonant natural frequency of thevibratory response characteristic of the system as a whole.

The shape of the velocity profile is selected in accordance with thefollowing criterion: The shape must be such that when the functionthereby defined is differentiated one or more times, no impulsivederivative occurs below the order of differentiation which correspondsto the second derivative of acceleration of cassette motion. If noimpulsive derivative occurs until one reaches even higher levels ofdifferentiation, so much the better. It is believed, however, that adesirable minimum is that no impulsive derivative occurs at an orderlower than the second derivative of the cassette acceleration.

In terms of mathematics, the reason for avoidance of impulsivederivatives in lower order derivatives of the motion specificationfunction is to cause the frequency domain spectrum amplitude of such afunction to drop off sharply, proceeding from zero frequency and tominimize the area under the curve of the frequency spectrum, which hasthe effect of reducing correspondingly the amount of energy availablefor system vibratory response.

Once the shape of the velocity profile has been selected in accordancewith the above criterion, the width of the profile, that is, totaltransit time T, is then selected or specified. T is specified inaccordance with the following criterion: A function is developedrelating T to the primary natural resonance frequency f of the system,such that in the frequency domain, the function defines a first relativenull which substantially coincides with the primary resonant naturalfrequency. In practice, such a function can be calculated using knownmathematics to arrive at an equation in the form of:

    T=a+bf+cf.sup.2 +df.sup.3 + . . . +nf.sup.m.

T, as mentioned above, represents the total transit time of cassettemotion. The coefficients a, b, c, d etc. are constant coefficients whosevalues are selected as a function of the mass of the cassette to bemoved.

Once the shape of the input wave form, corresponding to the velocitypulse, has been determined, as well as its width or time duration T, itis then necessary to adjust the amplitude of the actual voltage waveform applied to the servo system. This voltage wave form must beadjusted to an amplitude which is a function of the distance thecassette must travel in time T between its park and expose positions.This amplitude adjustment is also a function of the inherent electricaland mechanical properties of the cassette transport system, such asfriction, and the electrical characteristics of the power drive means.Accordingly, adjustment of the amplitude of the input wave form is mostadvantageously done by simple trial and error, which can easily be doneby one of ordinary skill.

DEVELOPMENT OF INPUT CONTROL FUNCTION CONFIGURATION IMPLEMENTING MOTIONSPECIFICATION

It is known that, as discussed above, means exist for conveying a filmbearing cassette from an x-ray shielded storage or park, position to anexposure position centered in an x-ray beam. The present invention isthus described in the context of a servo controlled spot film device. Anembodiment of the invention is implemented by modifying theservomechanism control electronics in a specific manner to generate acontrol input function which provides the appropriate motionspecification for reducing or eliminating residual vibratory response ofthe system as a whole.

The spot film device, and its attendant support structure, all of whichcomprise the x-ray examination apparatus, can be representedanalytically by a simple mass-spring model. It is well known that theresponse of a damped spring-mass system initially at rest and excited byan impulsive input is: ##EQU1## where: ##EQU2## with the above terms inequations (1) and (2) defined as:

F=force

W_(n) =natural frequency

t=time

T_(s) =damping ratio

m=mass

e=the exponential function

SIN=the trigonometric sine function

From the above relationships it is apparent that the residual vibrationdisplacement δ(t) is inversely proportional to mass; therefore, anycontrol method for moving a cassette is dependent upon the mass beingtransported. This mass is composed of the mass of the particularcassette being used and the mass of the moving parts of the transportmechanism. Here, the mass of the transport mechanism is constant, butthat of the cassette is widely variable, at the discretion of theapparatus operator, which variation occurs because of the use ofcassettes of different size.

The block diagram of FIG. 3 represents the structure of the x-rayexamination apparatus, where ω (the input) represents the angularvelocity of the cassette transport servomechanism drive motor whichmoves the cassette, and where δ (the output) represents the undesiredresidual vibration displacement. The symbol TF is the transfer functiondescribing system dynamic behavior over time. A purpose of the presentinvention is to specify w in such a way that δ is no greater than thelevel acceptable in the making of high quality diagnostic radiographicimages on film, assuming no other disrupting or disturbing influence onthe structure.

The block diagram of FIG. 4 represents the Fourier Transformationprocess as applied to the system represented in FIG. 3. ω(t) is the timedomain behavior function of motor angular velocity. ω(f) is, in turn,the frequency domain behavior of this same motor angular velocity.F[ω(t)]symbolically represents the mathematical process of performingknown Fourier Transformation.

With W(f) known, FIG. 3 can be translated into the terms illustrated inFIG. 5: that is, W(f) is as before, δ(f) is the frequency domainbehavior function of the residual vibration displacement; the term G(f)is the frequency response function which describes system dynamicbehavior over frequency.

A purpose of the invention, concurrent and compatible with the purposeas stated above, is to specify W(f) such that δ(f) is controlled in adesired manner.

The principles of motion specification can be applied to properlyspecify the configuration of the signal δ(t) or of its higherderivatives. Guiding insight in doing this, however, must first begained from inspection of the behavior of the corresponding frequencydomain signal.

In FIG. 6, all plots are frequency domain representations, with theabscissa in terms of frequency (typically expressed in cycles persecond, or Hertz) and the ordinates in terms of magnitude (typically inDecibels). FIG. 6(A) represents the case where the principles of motionspecification are not used. FIG. 6(b) represents the case where theprinciples of motion specification are applied with good effect, thisbeing an important aspect of the invention.

Plots 6(A)(1) and 6(B)(1) represent graphically the behavior of W(f).Plots 6(A)(3) and 6(B)(3) represent graphically the behavior of δ(f).

Plots 6(A)(2) and 6(B)(2) represent graphically the behavior of thefrequency response function G(f), and are identical. This function isunique to each x-ray examination apparatus and it decribes the resonantnatural response of the apparatus. This function need not be known indetail to successfully implement the present invention.

The derivation of the vibratory response characteristics of mechanicalsystems is discussed in detail in the following publication, which ishereby expressly incorporated by reference: Halvorsen, W. G., "ImpulseTechnique for Structural Frequency Response Testing", Sound andVibration, November, 1977, pp. 8-21 by PCB Piezotronics Inc., Buffalo,N.Y.

The general principles of transymmeteric motion specification arediscussed in the following publication, which is hereby expresslyincorporated by reference: Kramer, S.N., "Development Of TheVariable-Rate Transymmetric Motion With Discretely Vanishing Shock",Transactions of the ASME, Journal of Mechanisms, Transmissions, andAutomation in Design, Vol. 106, No. 1, pp. 109-113.

Reduction of residual vibration is discussed in the followingpublication, expressly incorporated by reference: Meckl, P. H., et al.,"Minimizing Residual Vibration For Point-To-Point Motion", Transactionsof the ASME, Journal of Vibration, Acoustics, Stress and Reliability inDesign, Vol. 107, No. 1, 1985, pp. 1-5.

If, as in the case of FIG. 6(A), no motion specification is applied tothe input to the system, then some energy associated with the input willcontribute to exciting the resonant response of the apparatus andobjectionable residual vibration displacements, δ(t), will result. Thissituation is avoided in FIG. 6(B), by applying a suitable motionspecification to the input.

While the plots of FIG. 6 are not intended as precise, but rather of aqualitative informational nature, the difference between the cases FIGS.6(A) and 6(B) can be easily discerned.

It is first noted in plots 6(A)(2) and 6(B)(2) that the function G(f)exhibits a primary natural resonant frequency easily identifiable by thepeak in each curve. Note further that the function ω(f) exhibits a peakat a frequency near the resonant frequency described in connection withG(f). The result, shown in FIG. 6(A)(3), is that the frequency plot ofactual vibratory motion shows a high spike in the neighborhood of theprimary natural resonant frequency which indicates that a large amountof energy is vibrating the structure of the radiographic spot filmdevice, probably blurring the image.

Referring, by contrast, to FIG. 6(B)(1), it will be seen that, byapplication of proper motion specification defining the function ω(f),residual vibration can be minimized. Note that the function ω(f) in FIG.6(B) contains a minimum of energy at a frequency in the neighborhood ofthe primary natural resonant frequency of the system as defined by thefunction G(f). As a result, the actual vibratory motion of the system,plotted in FIG. 6(B)(3), shows only a minor disturbance in theneighborhood of the primary natural resonant frequency of the system.

The diagrams of FIG. 7 depict a method of the specification of thecassette motion to minimize residual vibration of the system whichresults from such motion. In each case, the abscissa is time and theordinates are, respectively from bottom to top: second derivative ofacceleration (a); first derivative of acceleration (a), acceleration(a), velocity (v), and displacement (x), all pertaining to the linearmotion of the transported mass.

By suitably shaping (i.e., specifying) any one of these profiles,vibratory displacement δ(t) can be altered and controlled. In practice,it is convenient and expeditious to apply the motion specification tothe velocity (v) profile. This is true because the typical configurationof the servo electronics is voltage-mode; that is, voltage is thecontrolled variable and variation of voltage is directly proportional tovariation of steady state motor angular velocity (w), which is in turndirectly proportional to the linear velocity (v) of the transportedmass, by virtue of a linking mechanism between the motor output shaftand the cassette.

For best effect, however, it is preferable to first shape theacceleration (a) profile and accept the velocity (v) profile that isdictated by the acceleration time domain function, and only thenimplement the hardware for executing this particular velocity profilewhich results. The method for profile determination is further discussedbelow.

As shown in FIG. 7, an acceleration function is chosen which, in thetime domain, is substantially trapezoidal in shape.

The velocity (v) profile resultant from this choice of accelerationprofile and illustrated in FIG. 7 results from mathematical integrationof the trapezoidal acceleration (a) profile and is here termed the"transymmetric velocity pulse". Segments a-b, b-c, and c-d are describedmathematically as: ##EQU3##

As will be discussed, the choice of a trapezoidal acceleration functionfor cassette movement is a good one for reducing residual vibration. Thediscussion relating to FIG. 8, and the different acceleration profileshown there, along with the plots of FIG. 9, will assist in theundersanding the reasons for the superiority of the FIG. 7 accelerationprofile.

In FIG. 8, it is seen that, for a square acceleration profile, thesquare corners result in an impulsive derivative, (i.e., an undefinedspike) in the immediate next higher derivative (a). The impulse, in thisfigure is represented symbolically by arrows.

The diagrams of FIG. 9 depict the effect of the impulse on frequencydomain distribution of the profile. In FIG. 9(A) it is seen that thesquare profile exhibits impulsive behavior in the next higherderivative, and that the frequency spectrum of this profile, asdetermined by Fourier analysis, diminishes from zero frequency as theinverse power of one.

Referring again to FIG. 9, an alternate shape of profile, a triangle, isused. This profile exhibits impulsive behavior, not in the next higherderivative (a), but only in the second higher derivative (a). It is thusseen that this triangular profile has a frequency distribution spectrumwhich diminishes from zero frequency much faster than that of FIG. 9(a),i.e., as the inverse of the power of two.

The frequency spectrum behavior illustrated in FIG. 9(b) is a distinctimprovement over that illustrated in FIG. 9(a), because it is known,from Rayleigh's Theorem, that the integral of the frequency domainspectrum describing behavior of a mechanical system is related to themagnitude of energy of vibration of the system in the time domain.Accordingly, sharp diminution of the magnitude of the frequencies withrespect to distance from zero frequency suppresses the magnitude of theenergy of the system vibration at progressively higher frequencies.

It is thus apparent that the trapezoidal acceleration profile of FIG. 7is far superior to a lesser form such as the square acceleration profileof FIG. 8 by virtue of where the impulsive derivatives occur. In thetrapezoidal acceleration profile, the impulsive derivative occurs in ahigher order than in the case of the square wave. This results inreduced energy distribution with frequency, and a frequency spectrumhighly concentrated about the origin frequency of zero Hertz.

A representative frequency distribution spectrum (obtained by Fouriertechniques) for this transymmetric profile is depicted in FIG. 10. Afurther aspect of this invention is to now, having selected a velocityprofile shape such that the function does not become undefined beforebeing differentiated at least more than twice, formulate the timeduration of the transymmetric velocity pulse of FIG. 7 in such a manneras to cause the frequency of the first relative null, or minimum, of itsfrequency spectrum, labeled "a" in FIG. 10, to coincide with the primaryresonant natural frequency f of G(f) in FIG. 6. If this is done, theattenuated frequency distribution behavior depicted in the plot of FIG.6(B)(3) is achieved.

To achieve this goal it is important that a particular functionalrelationship between the transymmetric velocity pulse duration T andfrequency f, be utilized. For example, given one particulartransymmetric profile from among numerous variations, the functionalform defining the duration of the transit time T, for movement of acomponent of a given mass, is:

    T=824.32-129.29f+9.4010f.sup.2 -0.2659f.sup.3 -0.00288f.sup.4 +0.000307f.sup.5 -0.0000045f.sup.6                        (3)

A family of functions of this form exists, for each given imagingsystem, one equation for each discrete cassette mass which is to betransported. Once established for a selection of different masses to beused, these discrete equations relating T, or transit time, as afunction of frequency f, are susceptible of storage in an appropriatemeans, such as a section of known memory hardware dedicated to operationof the servo-mechanism of the radiographic system.

The coefficients of the T vs. f equations are functions, not directly,but only indirectly, of cassette mass. More specifically thesecoefficients are functions of the total vibratory responsecharacteristic of the entire system. The total vibratory response of thesystem is, however, itself in turn a function of cassette mass.

Stated another way, G(f) is a function of the dynamic response of thewhole system, which in turn is a function of cassette mass.

Known techniques of experimental modal analysis can be used to determinecharacteristics of the mechanical dynamic response of a system, and canbe repeated for each cassette intended for use.

Using such techniques, the primary resonant frequency of a given system,using a given cassette mass, is determined, and noted. Then, the chosenshape of the velocity pulse is analyzed mathematically, as describedbelow, by means including Fourier techniques, to determine just whatduration of the chosen shape of pulse will yield a pulse having afrequency spectrum whose first relative null coincides with thepreviously determined primary resonant frequency of the system inquestion, using the given cassette mass.

The Fourier analysis described in more detail below yields an equation Tvs powers of f having a unique set of coefficients a, b, c, d, etc.

A method of producing such a family of equations is discussed in thefollowing, here expressly incorporated by reference: Stojkov, M.,"Reduction of Residual Vibration of Robot Structures by ComputerControl" (Thesis at Clevelant State University, Cleveland, Ohio,U.S.A.).

The following is a general discussion on how the family of equations areobtained:

For reduced residual vibration performance it is desirable to have theresonant frequency coincide with a frequency null of the drive functionspectrum, eliminating excitation energy. The square wave spectrum, forinstance, exhibits the familiar humped behavior of the SINC function,also variously known as the filtering or interpolating function; thisfunction offers numerous possible nulls. To choose the proper one arelation between pulse duration and frequency is needed.

The closed-form analytic Fourier transform of the square pulse, (Hsu, H.P., "Fourier Analysis," rev. ed., Simon & Schuster, New York, 1970, p.78, incorporated by reference) with f(t) as unity over the integrationinterval is: ##EQU4##

Integration yields: ##EQU5## The relationship between pulse duration inthe time domain and frequency of the first spectral null derives fromEqn. (5). The function F(f)=0 when the argument of the sine term equalsn×Pi; n=1 for the first null, giving:

    T=1/f                                                      (6)

From this expression it is apparent that for a specific resonantfrequency a specific pulse duration (i.e., repositioning transit time)is required. For extremely low resonant frequency structure relativelylong (slow) pulses are necessary; higher resonant frequency structurestolerate faster pulses.

A relation analogous to Eqn. (6) is now needed for the transymmetricpulse. The analytic Fourier transform of the transymmetric pulse is notreadily available closed-form but can be approximated by a polynomialcurve fit method making use of the Derivative Theorem as shown inPapoulis, A., "The Fourier Integral And Its Applications," McGraw-Hill,New York, 1962, P. 53, incorporated by reference. The function beingtransformed is approximated, in the simplest form, by linear segments.This procedure is represented in FIG. 10A. Differentiating this polygonapproximation function twice yields a series of impulse functions:

    f(t)=ΣC.sub.i δ(t-T.sub.i)

The Fourier transform of this shifted impulse function is: ##EQU6##

The following transform pairs apply in the above integral (seeBracewell, R. N., The Fourier Transforms and its Applications, 2 ED.,McGraw-Hill, New York, 1978, ch. 1-8: ##EQU7## giving the followingresults: ##EQU8## A computer program can be developed to perform thisFourier transform, if desired, or the calculations can be done manuallyby one of ordinary skill. The frequency and time data from it can thenbe curve-fit by polynomial regression to give a more manageableexpression. FIG. 10B presents the results.

Comparison of the computed spectra of the square and transymmetricpulses, shown in FIG. 10, is instructive. For the square pulse animportant feature to note is that the steep flanks of the notchesleading to the nulls indicate a sensitivity to frequency variation.Depending upon the structure, this characteristic may be detrimental.With the transymmetric pulse an increase in bandwidth about the null isrealized, as well as a small decrease in frequency sensitivity. Theseaspects are apparent in the form of the peculiar shape of the spectrum.An additional hump has begun forcing its way into the notch, widening itand thus decreasing sensitivity to frequency variation over a limitedbandwidth. Admittedly, the spectrum magnitude behavior in this widenedfrequency zone is not flat, but nonetheless the magnitude of the energycontent is limited.

Adjusting a system's performance to take advantage of these spectralnulls requires adjustment of the repositioning move pulse duration. Iffor a given pulse duration the structure resonant frequency of interestfalls to the left of the first null in the spectrum, then the durationmust be increased to shift the null to lower frequencies. This inversebehavior follows directly from Eqn. (6). It is emphasized that theoptimum transit time is directly governed by the lowest resonantfrequency of the structure.

Referring again to FIG. 7, the plots of velocity (v) and displacement(x) result from the transymmetric acceleration specification being atrapezoidal function, and they are descriptive of transport of someparticular mass over specific distance X₁. To move this mass some lesserdistance, for example, X₂, while keeping the same trasnit time durationT, the transymmetric velocity (v) pulse is reduced correspondingly inamplitude.

FIG. 11 illustrates a practical embodiment of the servo system accordingto the present invention. It is to be understood, however, that thepresent invention is not limited to the specific implementationsillustrated in FIG. 11.

A microprocessor 100 controls the operations of the spot film device. Aportion of the capacity of the microprocessor is dedicated to high levelcontrol of the electro-mechanical servo mechanism.

Representations of the family of equations (3) in the form as describedabove are stored in the microprocessor for use in operating the cassettetransport system for each different cassette selected. As the mass to betransported changes due to selection of different sized cassettes, themicroprocessor determines the required transit time T, by appyling theone of the family of equations in the form such as (3) which is derivedfor the particular cassette mass selected.

A digital electronics servo controller 102, of known design,accommodates both position and velocity feedback.

Computer capacity is provided by a dedicated controller memory 104associated with the servo controller. It is in the memory 104 that thetransymmetric velocity profile data of equations (4) reside. The servocontroller 102 consults the controller memory containing datarepresenting the shape of the desired velocity profile and eitheracquires or calculates the velocity profile data with the transit timeT, as selected by the microprocessor.

The servo controller then outputs the velocity profile as an electricalvoltage time varying drive signal 106. The drive signal is converted bya digital to analog converter 108, and fed to a speed amplifier 110.From the amplifier 110 the signal is transmitted through a switch 112 toa power amplifier 114 providing power to a motor 116. The poweramplifier amplifies the velocity profile signal and drives the servomotor accordingly. In this manner the mass to be transported is made totravel to the expose position from the park position with a unique andparticular triangular velocity profile which minimizes structuralvibration. The mass to be moved is represented by the box designated120.

When switch 112 is in its upper position, contacting terminal 122, themotion of the mass being transported is controlled in an "open loop"manner.

A position sensor 124 and a velocity sensor 126 are also provided.During transport the position and velocity sensors return respectivelyfeedback signals through amplifiers 128 and 130. Signals from theamplifiers 128, 130 are directed through analog to digital converters132, which return the digital information to the servo controller 102,which monitors these signals.

During the terminal phase of cassette transport, i.e., the last two orthree percent of the transport distance as determined by the positionfeedback signal, the servo controller actuates the switch 112 to move toits downward position to contact the terminal 136. The control systemoperates in the closed loop fashion for the last two or three percent ofcassette travel as the position and/or velocity feedback signals assumecontrol authority in known fashion as the transported mass comes to restat the expose position at the end of its travel.

Another feasible embodiment involves continuous closed loop operation.In this mode of operation the switch 112 is permanently set to engagethe terminal 136, or the switch 112 is omitted altogether. The positionand velocity feedback signals pass through appropriate amplifiers andare then transformed by the analog to digital converters. These digitalposition and velocity signals are transmitted to the servo controller102 which generates a digital error signal. In this case the velocityerror signal is the primary control signal. The position error signal isredundant but it may be used as a second control parameter to gain ahigher degree of control over the system. It is understood that thecontroller memory 104 provides the appropriate velocity profile to serveas the reference signal in closed loop operation. The servo controllerdigitally combines the velocity feedback signal with the referencesignal to create the error signal in accordance with known feedbackcontrol technique. The velocity error signal is digital to analogconverted and sent sequentially to amplification circuitry. Thus, themotor 116 is driven such that its rotational velocity profilecorresponds to the reference profile, within the limits of prescribederror bounds.

By operating in an open loop manner, when this mode is chosen, themotion specification technique strives to beneficially control, at theoutset of motion, the input energy and vibration of the system, and toavoid undesired system vibratory response a priori.

This open loop operating characteristic, and the ability of embodimentsof the present invention to prevent undesirable vibratory response fromoccurring in the first place, illustrates an important aspect of thisinvention and an important advantage over the prior art. In the priorart closed loop servo and other methods, such as motor reversal, varioustypes of shock absorbers, etc., are employed to mitigate, after thefact, the undesired vibratory response of this same input energy. Thus,it could be said that the prior art devices are curative in nature,while the embodiments of the present invention are preventive.

In accordance with another embodiment of the invention, a mechanicallinkage including a cam is interposed between the servo drive motor andthe movable cassette in order to impart motion to the cassette. Themechanical linkage defines, in the time domain, a sinusoidalacceleration function over the path of cassette movement between thepark and expose positions.

FIG. 12 illustrates such an embodiment. In FIG. 12, a cam 200, havingdefined in its upper surface a cam groove 202, is pivoted about a pivotpoint 204 for rotative motion about the pivot 204. The rotative motionis about an axis perpendicular to the paper as shown in FIG. 12.

A gear segment arm 206 is pivotally mounted about a pivot point 208 forpivotal motion about an axis perpendicular to the plane of the paper inFIG. 12. The gear segment arm bears a cam follower 210 which is engagedto ride in the cam groove 202 of the cam 200. The outer end of the gearsegment arm 206 defines a gear segment 212. A pinion gear 214 ispivotally mounted for rotation about a pivot point 216. The teeth of thepinion gear 214 engage the teeth of the gear segment 212. A drive arm218 is mounted for rotational motion in unison with the pinion gear 214.

FIG. 12 illustrates a radiographic film cassette 220 having a generallyrectangular configuration and which rides along a set of tracks 222which define its path of motion between the park and expose positions.The drive arm 218 is pivotally mounted to the cassette at a point 224,such that, when the drive arm 218 rotates about the pivot 216 in unisonwith the pinion gear 214, the cassette 220 is caused to move along thetracks 222. In the direction generally indicated by the arrows 226. Aslot 228 is defined in the cassette carriage in order to permit relativemotion of the pivot point 224 to the right and left as shown in FIG. 12as the drive arm 218 rotates.

Rotation of the drive arm 218 is, as mentioned above, achieved in unisonwith rotation of the pinion gear 214 abouts its pivot 216. The piniongear is caused to be rotated by rotation of the gear segment arm 206about its pivot 208 in the direction indicated by the arrows 230.

Rotation of the gear segment arm 206 about its pivot 208 is caused byrotation of the cam 200 about its pivot 204 in a direction indicated bythe arrows 232. This rotation results because of the cooperation of thecam follower 210 riding in the cam groove 202 as the cam rotates. Whilethe configuration of the cam groove 202 in FIG. 12 is of a generalnature, and not precisely indicative of the actual shape of the camgroove, it can be seen from FIG. 12 that as the cam 200 rotates the camfollower will be moved toward or away from the cam pivot point 204,depending upon the direction of cam rotation. This radial procession ofthe cam follower as the cam rotates causes the motion of the gearsegment arm 206 in the direction indicated by the arrows 230.

The cam is driven by a reversible electric motor, which is of knowndesign and is not illustrated in FIG. 12.

In order to more clearly indicate the iterrelation of the mechanicaldrive parts, FIG. 12 is not drawn to scale. The actual dimensions of thevarious parts and their action is set forth immediately below.

In the preferred embodiment, the distance between the pivots 216, 224 isapproximately 35 millimeters. The pinion gear 214 has a diameter ofapproximately 44 millimeters. The gear ratio between the pinion gear 214and the gear segment 212 is approximately 4:1. The distance between theteeth of the gear segment 212 and the pivot 208 is approximately 9.8millimeters. The diameter of the cam 200 is approximately 22.2millimeters. The motor causes the cam to rotate at approximately 20revolutions per minute. In moving the cassette 220 between its park andexpose positions, the angle φ varies, as shown in FIG. 12 by about 90degrees, and the cam angle rotation θ by about an increment of 180°.

In the preferred embodiment, the location of the cam groove is definedby the following relations: ##EQU9## As can be seen from the aboveequations, the cam groove 202 defines a dwell time of uniform radiusnear each end of the cam groove.

Referring again to FIG. 12 the cam 200 defines an ear portion 240 at itsouter edge. The ear portion 240, at predetermined points of camrotation, engages respectively limit switches 242, 244. When the ear 240engages one of the limit switches 242, 244, the motor driving the cam isdeactuated. The limit switches 242, 244 are fixed at locations such thatthe motor is deactuated during the dwell time at either of the ends ofcam motion as defined by the groove.

In the preferred embodiment, the cam groove defines a cycloidalfunction. It is to be understood, however, that other functions could beused as well, such as a modified sine function, or a polynomialfunction.

Referring again to FIG. 12, spring detent means is provided to lock thecassette affirmatively when it reaches one of the end positions of itsdefined movement. Only one such spring detent means is illustrated inFIG. 12, but it is to be understood that a second detent spring meanscould also be employed.

More specifically, the edge of the cassette carriage 220 defines a smallV-groove 250, which can accommodate a detent ball 252. A spring means254 is mounted to a fixed structure 256, and serves to resiliently biasthe ball 252 toward the right as shown in FIG. 12. Thus, when thecassette reaches a point at which the V-groove 250 is aligned with theball 252, the cassette becomes locked at that position of movement.

The spring detent means serves to minimize any back lash in cassettemotion which might otherwise result from unavoidable slack in the drivemechanism as illustrated in FIG. 12.

Optionally, overload protection can be employed for the system byinterposing a slip clutch, or some equivalent structure, between themotor and the cam 200.

Optionally, a known brake means could be employed to assist inmechanically or electrically braking the cassette as it nears an end ofits travel path.

The design of modeled cam systems is discussed in the followingpublication, which is hereby expressly incorporated by reference: Tesar,D., et al., "The Dynamic Synthesis, Analysis, and Design of Modeled CamSystems", pp. 54-69, Lexington Books, Lexington, Mass., 1976.

Cam design is also discussed in the following publication, alsoexpressly incorporated by reference: Rothbart, H. A., "Cams", John Wileyand Sons Inc., New York, pp. 42-45.

It is to be understood that the disclosure of the embodiments of thisinvention set forth herein is intended as illustrative, rather thanexhaustive, of the invention. It is to be recognized that those ofordinary skill in the relevant art may be able to make certain additionsto, deletions from, or modifications to the embodiments set forth inthis disclosure without departing from the spring or the scope of theinvention, as set forth in the appended claims.

We claim:
 1. A medical diagnostic imaging system comprising:(a) an x-raysource; (b) film means responsive to x-rays for producing an imagetherefrom; (c) a cassette carriage for accommodating a radiographic filmcassette including a portion of said film; (d) means for mounting saidcarriage for movement along a path between first and second positions;(e) electromechanical apparatus and circuitry including an electricmotor for driving cassette movement between said first and secondpositions; (f) circuitry for applying to said motor an electrical inputwaveform, said waveform defining in the time domain a concave upsegment, a substantially linear positively sloping segment followingsaid concave up segment, a concave down peak segment following saidpositively sloping substantially linear segment, a negatively slopingsubstantially linear segment following said concave down peak segmentand another concave up segment following said substantially linearnegatively sloping segment.
 2. The system of claim 1, wherein:(a) saidfirst concave up segment of said input waveform conforms to thefollowing equation: ##EQU10## (b) said substantially linear positivelysloping segment conforms to the following equation:

    v=A(t-.sub.2.sup.t 1)

(c) said concave down peak segment conforms to the following equation:##EQU11## where A is a constant, t is time, t₁ is a first time and t₂ isa second time subsequent to t₁.
 3. The system of claim 1, furthercomprising:means for adjusting the time duration of said input waveform.4. The system of claim 1, wherein:said input waveform defines in thefrequency domain a first relative null which substantially coincideswith the primary resonant natural frequency of said system.
 5. Thesystem of claim 1, further comprising:means for adjusting the amplitudeof said input waveform.
 6. The system of claim 1, furthercomprising:closed loop servo circuitry coupled for actuating saidelectric motor.
 7. The system of claim 6, further comprisingcircuitryfor selectively opening the closed loop feedback circuit to bring aboutopen loop operation.
 8. A method of controlling motion of a filmcassette carriage in a medical diagnostic imaging system, said systemincluding an x-ray source and structure for mounting said film cassettecarriage for movement along a path between first and second positions,an electric motor and mechanical drive linkage for providing power formoving said cassette carriage along said path, said method forcontrolling movement of said carriage comprising the steps of:(a)generating and applying to an input of said electric motor an inputelectrical signal defining a predetermined waveform, said waveformincluding in the time domain a concave up segment, a substantiallylinear positively sloping segment following said concave up segment, aconcave down peak segment following said positively slopingsubstantially linear segment, a negatively sloping substantially linearsegment following said concave down peak segment and another concave upsegment following said substantially linear negatively sloping segment.9. The method of claim 8, further comprising the step of:adjusting thetime duration of said input waveform.
 10. The method of claim 8, furthercomprising the step of:adjusting the amplitude of said input waveform.